1. Field of the Invention
The present invention relates to a method and a unit for calculating a degradation degree of a battery to supply an electrical power to a load.
2. Related Art
A battery is an electrical source for starting an engine, operating on-vehicle electrical equipment, etc. so that it is important to know a charged state of the battery.
However, the battery repeats charging and discharging, which increases an inner impedance thereof to gradually decrease a discharging capacity and a full charged capacity.
Thus, to correctly know a charged state of the battery, it is necessary to find its present full charging capacity. Therefore, it is important to find a latest degradation state of the battery which appears with its repeated charging and discharging operations.
For knowing the degradation degree of the battery, an original full charging capacity is measured when the battery is new, and the original full charging capacity is compared with a present full charging capacity of the battery. Conventionally, a battery is completely discharged from its full charged state, while a discharge current value and a discharge time are measured to obtain a discharging current capacity which is considered as a present capacity of the battery.
In a vehicle having an ordinary engine and in a hybrid vehicle having a motor generator which acts at an insufficient torque state of an engine, a battery needs to output a large quantity of power at the initial starting of the engine. After the starting, an alternator or the motor generator provides an electrical power to charge the battery into a full charged state during an operation state of the vehicle.
In this vehicle, to know a present full charge capacity of the battery, it is necessary to remove the battery from the vehicle to completely discharge the battery from its full charged state. This work is unpractical and disadvantageous.
Therefore, to monitor a degradation degree of the battery in a state where the battery has been mounted on the vehicle, factors varying with the degradation degree of the battery are measured. This is important to know a present degradation degree of the battery.
One of the factors varying with the degradation degree of the battery is a concentration polarization impedance (combined resistance). The concentration polarization impedance causes a voltage drop between a pair of terminals of the battery. The voltage drop consists of an IR loss (base resistance, i.e. a voltage drop due to an ohmic resistance) and a voltage drop due to a polarization resistance (activation polarization and concentration polarization) related to a chemical reaction.
Thus, a present degradation degree of the battery can be known by monitoring how the base resistance, the activation polarization, and the concentration polarization resistance vary from their original values to drop the terminal voltage of the battery.
A degradation of such a battery is due to increase of the base resistance, the activation polarization resistance, or the concentration polarization resistance. Therefore, it is insufficient to find only one of the degradations to determine the state of the battery. For example, the base resistance varies little in a charged state (SOC) more than 40%, while the base resistance varies sharply in a SOC less than 40%. In the meantime, the activation polarization resistance and the concentration polarization resistances increase apparently even in a SOC more than 40%.
Thus, the base resistance, the activation polarization resistance, and the concentration polarization resistance do not vary with an apparent regularity in connection to the degradation degree of the battery. However, there are relations among the base resistance, the activation polarization resistance, and the concentration polarization resistance. Therefore, it is necessary for determining a correct degradation state of the battery to monitor all of the base resistance, the activation polarization resistance, and the concentration polarization resistance.
In view of the aforementioned situation, an object of the invention is to provide a method and a unit for determining a degradation degree of a battery to supply an electrical power to a load. The method considers relations among a base resistance, a activation polarization resistance, and a concentration polarization resistance of the battery. A measurement of the battery is made while the battery is kept at a usage position.
A first aspect of the invention is a degradation degree computing method for a battery for supplying an electrical power to a load, the method comprising the steps of:
a first step for obtaining a base resistance of the battery by cyclically measuring a discharge current and a voltage between a pair of terminals of the battery while a rush current is flowing in an electric load electrically connected to the pair of the terminals, the rush current simply decreasing from a peak to a constant value after the rush current simply increases from zero to the peak,
a second step for obtaining at least one of a concentration polarization resistance and an activation polarization resistance of the battery from the discharge current and the terminal voltage that are measured in the first step,
a third step for obtaining a degradation degree of the base resistance which is a ratio of the base resistance obtained by the first step to an original base resistance of the battery,
a fourth step for obtaining a polarization resistance degradation degree which is a ratio of one of the concentration polarization resistance and the activation polarization resistance to an original polarization resistance, and
a fifth step for obtaining a degradation degree of the battery by multiplying the degradation degrees of the base resistance and the polarization resistance together. Thus, even when there is a relation between the base resistance and the polarization resistance, the degradation degree of the battery is calculated to include the relation.
Preferably, the second step obtains each of a concentration polarization resistance and an activation polarization resistance of the battery, and the fourth step obtains a concentration polarization resistance degradation degree which is a ratio of the concentration polarization resistance obtained in the second step to an original concentration polarization resistance of the battery, the fourth step also obtaining an activation polarization resistance degradation degree which is a ratio of the activation polarization resistance obtained in the second step to an original activation polarization resistance of the battery, wherein the polarization resistance degradation degree of the fifth step is obtained by multiplying the degradation degrees of the concentration polarization resistance and the activation polarization resistance together. Thus, even when there is a relation between the concentration polarization resistance degradation and the activation polarization resistance degradation, the degradation degree of the battery is calculated in consideration of the relation.
A second aspect of the invention is a degradation degree computing unit of a battery for supplying an electrical power to a load. As illustrated in FIG. 1, the unit includes:
a measuring means 23a-1 for measuring a discharge current and a voltage between a pair of terminals of the battery while a rush current is flowing in an electric load electrically connected to the pair of the terminals, the rush current simply decreasing from a peak to a constant value after the rush current simply increases from zero to the peak,
a base resistance computing means 23a-2 for obtaining a base resistance of the battery from the discharge current and the voltage that are measured by the measuring means,
a polarization resistance computing means 23a-3 for obtaining at least one of a concentration polarization resistance and an activation polarization resistance of the battery from the discharge current and the terminal voltage that are measured by the measuring means,
a base resistance degradation degree computing means 23a-4 for obtaining a degradation degree of the base resistance which is a ratio of the base resistance obtained by the first step to an original base resistance of the battery,
a polarization resistance degradation degree computing means 23a-5 for obtaining a polarization resistance degradation degree which is a ratio of one of the concentration polarization resistance and the activation polarization resistance to an original polarization resistance, and
a battery degradation degree computing means 23a-6 for obtaining a degradation degree of the battery by multiplying the degradation degrees of the base resistance and the polarization resistance together. Thus, even when there is a relation between the base resistance and the polarization resistance, the degradation degree of the battery is calculated in consideration of the relation.
Preferably, the polarization resistance computing means calculates each of a concentration polarization resistance and an activation polarization resistance of the battery, and the polarization resistance degradation degree computing means calculates a concentration polarization resistance degradation degree which is a ratio of the concentration polarization resistance obtained in the second step to an original concentration polarization resistance of the battery, the polarization resistance degradation degree computing means also calculating an activation polarization resistance degradation degree which is a ratio of the activation polarization resistance obtained in the second step to an original activation polarization resistance of the battery, wherein the battery degradation degree computing means obtains a degradation degree of the battery by multiplying the degradation degrees of the base resistance, the concentration polarization, and the activation polarization one another. Thus, even when there is a relation between the concentration polarization resistance degradation degree and the activation polarization resistance degradation degree, the degradation degree of the battery is calculated in consideration of the relation.
For example, the original base resistance is obtained from one of computing methods described hereinafter.
In a first computing method for obtaining the base resistance of the battery, a discharge current and a voltage between a pair of terminals of the battery are measured while a rush current is flowing in an electric load electrically connected to the pair of the terminals, the rush current simply decreasing from a peak to a constant value after the rush current simply increases from zero to the peak. A first approximate equation showing a correlation between the current and the voltage is obtained in a region where the discharge current is increasing, and a second approximate equation showing a correlation between the current and the voltage is obtained in a region where the discharge current is decreasing. A voltage drop due to the concentration polarization of the battery is considered to be deducted from the first and second approximate equations if necessary. At the peak of the rush current, a differential of the voltage relative to the current is obtained for each of the first and second approximate equations. An intermediate value of thus obtained voltage differentials is determined as the base resistance of the battery. Thus, in a normal operation state of the load, an electrical power is supplied to the load to measure a terminal voltage and a discharge current of the battery. This can obtain a base resistance of the battery.
In a second computing method for obtaining the base resistance of the battery, the obtained voltage differentials are averaged to obtain the base resistance of the battery. Thus, when each of the first and second approximate equations gives a differential substantially the same as each other regarding the activation polarization at the peak, a mean value of differentials of the first and second approximate equations at the peak point is determined as the base resistance of the battery.
In a third computing method for obtaining the base resistance of the battery, the voltage differentials obtained by the first computing method are averaged to determine the base resistance in consideration of lengths of the increasing and decreasing regions of the rush current. Thus, the intermediate value is obtained in consideration of a relation between the activation polarization and the concentration polarization to obtain the base resistance of the battery.
In a fourth computing method for obtaining the base resistance of the battery, each of the first and second approximate equations is a quadratic equation. Thus, the intermediate value is calculated from differentials of the first and second approximate equations at the peak point to obtain the base resistance of the battery.
In a fifth computing method for obtaining the base resistance of the battery, according to each of the first and second approximate equations of the fourth computing method, a terminal voltage is calculated at a zero point of the discharge current. The difference between the two voltages is considered to be a voltage drop due to a concentration polarization of the battery. Constant coefficients of the first approximate equation are determined by deducting the voltage drop due to the concentration polarization of the battery. Thus, a first approximate equation, in which an effect of the concentration polarization of the battery is correctly removed, is obtained.
In a sixth computing method for obtaining the base resistance of the battery which is a modification of the fifth computing method, constant coefficients of the second approximate equation are determined from three voltage values between zero and the peak of the discharge current including a voltage value at the peak. Thus, the second approximate equation, in which a voltage drop of the concentration polarization of the battery is removed, is obtained with ease.
In a seventh computing method for obtaining the base resistance of the battery which is a modification of the sixth computing method, the intermediate value which is determined as the base resistance may be obtained in consideration of differentials of the first and second approximate equations at the peak. Thus, the base resistance is calculated with ease.
In an eighth computing method for obtaining the base resistance of the battery which is a modification of the sixth computing method, constant coefficients of the second approximate equation are determined from three voltage values between zero and the peak of the discharge current including a voltage value at the zero point of the discharge current. Thus, the zero point which includes basically no effect of the concentration polarization is effectively used for obtaining the approximate equation.
In a ninth computing method for obtaining the base resistance of the battery which is a modification of the fifth computing method, a voltage is obtained at a middle point between zero and the peak of the discharge current. A line connecting the peak point with the middle point may be utilized to interpolate the intermediate value. Thus, the intermediate value is calculated with ease.
In a tenth computing method for obtaining the base resistance of the battery which is a modification of the fifth computing method, a first current-time integral is calculated between zero and the peak of the discharge current, and a second current-time integral is calculated between the zero point and a distal zero point positioned after the peak of the discharge current. A ratio of the current-time integral to the second current-time integral is calculated. The voltage drop between the initial zero point and the peak due to the concentration polarization maybe obtained by multiplying the ratio and the difference of the voltages obtained by the first and second approximate equations at the initial zero point of the discharge current. Thus, a voltage at the peak, which does not include a voltage drop due to the concentration polarization of the battery, is obtained.
In an eleventh computing method for obtaining the base resistance of the battery which is a modification of the first computing method, when the load provides a rush current which increases linearly up to the peak within a short time without occurrence of a concentration polarization, the first approximate equation is linear. The linear equation may be used to obtain the intermediate value. Thus, the approximate equation and the intermediate value are obtained with ease.
For example, original and present concentration polarization resistance values of a battery are obtained from one of computing methods described hereinafter.
In a first computing method for obtaining the concentration polarization resistance of the battery, a discharge current and a voltage between a pair of terminals of the battery are measured while a rush current is flowing in an electric load electrically connected to the pair of the terminals, the rush current simply decreasing from a peak to a constant value after the rush current simply increases from zero to the peak. A first approximate equation showing a correlation between the current and the voltage is obtained in a region where the discharge current is increasing, and a second approximate equation showing a correlation between the current and the voltage is obtained in a region where the discharge current is decreasing. A voltage is obtained from each of the first and second approximate equations at a point where the discharge current is zero. The deference between the two voltages obtained by the first and second approximate equations at the point where the discharge current is zero is calculated. The deference is determined to be a total voltage drop due to a concentration polarization of the battery. The concentration polarization occurs with the rush current. A voltage drop due to the concentration polarization at any point of the discharge current is obtained in use of the deference. From the voltage drop, a concentration polarization resistance value of the battery is obtained at any point of the discharge current.
In a second computing method for obtaining the concentration polarization resistance of the battery, a voltage drop due to the concentration polarization at the peak of the rush current is obtained in use of the deference. A concentration polarization resistance is calculated from the voltage drop.
In a third computing method for obtaining the concentration polarization resistance of the battery, a discharge current and a voltage between a pair of terminals of the battery are measured while a rush current is flowing in an electric load electrically connected to the pair of the terminals, the rush current simply decreasing from a peak to a constant value after the rush current simply increases from zero to the peak. A first approximate equation showing the correlation between the current and the voltage is obtained in a region where the discharge current is increasing, and a second approximate equation showing a correlation between the current and the voltage is obtained in a region where the discharge current is decreasing. Each voltage is obtained from each of the first and second approximate equations at a point where the discharge current is zero. The deference between the two voltages at the point where the discharge current is zero is calculated. The deference is determined to be a total voltage drop due to a concentration polarization of the battery. A voltage drop at the peak due to a concentration polarization of the battery is obtained by multiplying the total voltage drop by a time ratio which is a ratio of an increasing time from zero to the peak of the rush current to a total time corresponding to the total voltage drop. A voltage drop due to the concentration polarization at any point of the discharge current between the initial zero point and the peak is obtained in use of the voltage drop value at the peak in use of a linear relation of the voltage and a corresponding elapsed time. From the voltage drop, a concentration polarization resistance value of the battery is obtained at any point of the discharge current between the initial zero point and the peak.
In a fourth computing method for obtaining the concentration polarization resistance of the battery, a voltage drop due to the concentration polarization at any point of the discharge current between the peak and the last zero point is obtained from the voltage drop value at the peak in use of the linear relation of the voltage and a corresponding time elapsed from the peak.
Concerning the first to fourth computing methods for obtaining the concentration polarization resistance of the battery, a voltage drop due to factors other than the concentration polarization can be calculated. The voltage drop is obtained by deducting a voltage drop due to a concentration polarization of the battery from the first and second approximate equations.
For example, original and present activation polarization resistance values of a battery are obtained by a computing method described hereinafter.
In the first and second approximate equations obtained in the fifth concentration polarization resistance computing method, a voltage drop due to a base resistance of the battery is deducted. Thus, first and second approximate equations for a voltage drop due to the activation polarization of the battery are obtained. Thereby, a voltage deduction and an associated activation polarization value at any current point due to the activation polarization can be easily calculated in use of the first and second approximate equations.
For example, an original base resistance and a base resistance with a degradation degree are obtained from a computing device described hereinafter.
As illustrated in a basic block diagram of FIG. 2, a computing device for obtaining a base resistance of the battery has a current and voltage measuring means 23a-1 for cyclically measuring a discharge current and a voltage between a pair of terminals of the battery, while a rush current is flowing in an electric load electrically connected to the pair of the terminals, the rush current simply decreasing from a peak to a constant value after the rush current simply increases from zero to the peak. The computing device further has an approximate equation generating means 23a-7 including a first approximate equation showing a correlation between the current and the voltage in a region where the discharge current is increasing and a second approximate equation showing a correlation between the current and the voltage in a region where the discharge current is increasing. A voltage drop due to a concentration polarization of the battery is deducted from the first and second approximate equation if necessary. At the peak of the rush current, a differential of the voltage relative to the current is obtained for each of the first and second approximate equations. The computing device further has a base resistance computing means 23a-8 in which a intermediate value of thus obtained voltage variations is determined as a base resistance of the battery. Thus, in a normal operation state of the load, an electrical power is supplied to the load to measure a terminal voltage and a discharge current of the battery. This can give a base resistance of the battery.
For example, a concentration polarization resistance of a battery is obtained in its original or present state from one of computing devices described hereinafter.
In a first computing device for obtaining a concentration polarization resistance of the battery, as shown in a basic block diagram of FIG. 3, a current and voltage measuring means 23a-1 obtains a discharge current and a voltage between a pair of terminals of the battery while a rush current is flowing in an electric load electrically connected to the pair of the terminals, the rush current simply decreasing from a peak to a constant value after the rush current simply increases from zero to the peak. The first computing device further has an approximate equation generating means 23a-7 including a first approximate equation showing a correlation between the current and the voltage in a region where the discharge current is increasing and a second approximate equation showing a correlation between the current and the voltage in a region where the discharge current is decreasing. The first computing device further has a concentration polarization resistance computing means 23a-9, in which each voltage is obtained from each of the first and second approximate equations at a point where the discharge current is zero. The deference between the two voltages at the point where the discharge current is zero is calculated. The deference is determined to be a total voltage drop due to a concentration polarization of the battery. The concentration polarization occurs with the rush current. A voltage drop due to the concentration polarization at any point of the discharge current is obtained in use of the deference. From the voltage drop, a concentration polarization resistance value of the battery is obtained at any point of the discharge current.
In a second computing device for obtaining the concentration polarization resistance of the battery, as shown in a basic block diagram of FIG. 3, a current and voltage measuring means 23a-1 obtains a discharge current and a voltage between a pair of terminals of the battery while a rush current is flowing in an electric load electrically connected to the pair of the terminals, the rush current simply decreasing from a peak to a constant value after the rush current simply increases from zero to the peak. The second computing device further has an approximate equation generating means 23a-7 including a first approximate equation showing a correlation between the current and the voltage in a region where the discharge current is increasing and a second approximate equation showing a correlation between the current and the voltage in a region where the discharge current is decreasing. The second computing device further has a concentration polarization resistance computing means 23a-10, in which each voltage is obtained from each of the first and second approximate equations at a point where the discharge current is zero. The deference between the two voltages at the point where the discharge current is zero is calculated. The deference is considered to be as a total voltage drop due to a concentration polarization of the battery. A voltage drop at the peak due to a concentration polarization of the battery is obtained by multiplying the total voltage drop by a time ratio which is a ratio of an increasing time from zero to the peak of the rush current to a total time corresponding to the total voltage drop. A voltage drop due to the concentration polarization at any point of the discharge current between the initial zero point and the peak may be obtained from the voltage drop value at the peak in use of a linear relation of the voltage and a corresponding elapsed time. From the voltage drop, a concentration polarization resistance value of the battery is obtained at any point of the discharge current between the initial zero point and the peak.
For example, an activation polarization resistance of a battery is obtained in its original or present state from one of computing devices described hereinafter
As illustrated in a block diagram of FIG. 4, an activation polarization resistance computing device has a modified approximate equation generating means 23a-11 for providing first and second approximate equations which are obtained by deducting a voltage drop due to the concentration polarization from the first and second approximate equations. The activation polarization resistance computing device has a concentration polarization approximate equation generating means 23a-12 including concentration polarizations approximate equations which are obtained by deducting each of the first and second approximate equations of the modified approximate equation generating means 23a-11 from each of the first and second approximate equations of the approximate equation generating means 23a-7. The concentration polarization approximate equations can give a voltage drop due to the concentration polarization at any current point of the battery. The activation polarization resistance computing device further has an approximate equation generating means 23a-13 for obtaining first and second activation polarization approximate equations by deducting a voltage reduction due to the base resistance from the first and second approximate equations provided by the modified approximate equation generating means 23a-11. The activation polarization resistance computing device further has an activation polarization resistance computing means 23a-14 for obtaining an activation polarization resistance value of the battery at a desired current. That is, a voltage drop at the desired current is calculated by the approximate equation of the activation polarization, and an activation polarization resistance is calculated from the voltage drop.
As mentioned above, each voltage is obtained from each of the first and second approximate equations at a point where the discharge current is zero. The deference between the two voltages at the point where the discharge current is zero is calculated. The deference is determined to be a total voltage drop due to a concentration polarization of the battery. A voltage drop at the peak due to a concentration polarization of the battery is obtained by multiplying the total voltage drop by a time ratio which is a ratio of an increasing time from zero to the peak of the rush current to a total time corresponding to the total voltage drop. A voltage drop due to the concentration polarization at any point of the discharge current between the initial zero point and the peak is obtained from the voltage drop value at the peak in use of a linear relation of the voltage and a corresponding elapsed time. From the voltage drop, a concentration polarization resistance value of the battery is obtained at any point of the discharge current between the initial zero point and the peak.